So, in effect, energy has to be stored during the day, and used during "unsunny" times.
Where I live we already have a pump-storage scheme in place. During the night, when demand for electricity is low, water is pumped uphill from one dam to another. During periods of high demand (typically early morning, and evening) water is released generating hydro-power to supplement the grid. It generates about 400MW of power - suitable for supplementing a city, but not for taking it "off the grid". It also doesn't scale particularly well - a 4GW plant would take a lot of water.
However, all is not lost. With "free" electricity it's fairly easy to split water into hydrogen and oxygen. Hydrogen isn't the easiest, or least damaging substance to work with, but it is certainly clean, storable, transportable and so on.
A power plant burning hydrogen as the fuel can run day and night. And a "hydrogen reservoir" would act as a natural capacitor - able to smooth the supply of energy to the plant.
Of course there are lots of uses for electricity which are not time-of-day sensitive. Desalination for example allows dry coastal regions (which usually get a lot of sun, and hence why they're dry in the first place) to become irrigated.
Solar power is a lot more useful than just domestic use, and I for one look forward to the day when it's cheap.